curve #4132

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y² = x³ + x² − 876495501925960172907739427448182496740x + 9998729527643225776153436333560836124638629326004322483744

a-invariants: [0, 1, 0, -876495501925960172907739427448182496740, 9998729527643225776153436333560836124638629326004322483744]
c-invariants: [42071784092446088299571492517512759843536, -8638902311883747070848999696751238941485204692772811185016000]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 133996739179604853376441920740335466697039854538683697168681882630205841173122944135042369279112
discriminant (Δ): -93809082580103622721293294716704112072011379078068754181884602442090755042691724646163608014497915076471141633070848
Faltings height: 21.1617
naive height: 280.6228
primes of bad reduction: 2, 3, 13, 19, 23, 37, 47, 53, 59, 108011, 7289864262035106006665351, 229532034922708058774366425215308148929207242484091331
regulator: 670975407266209212319832523.004198615676995286530136432654914084104243965409081686907012246
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 00:57:15 UTC
last updated: 2026-10-11 00:57:15 UTC

Witness: 26 independent points log in to add more points →

(-1957659040029143317748/121, 187970635008044949571440736746264/1331)
(10669592379837109846, -43145200733448185086719435966)
(-567600323866231675877171/21316, 374202264036726533513864336480647797/3112136)
(165095521173434513415358/10609, 12337249029116528961178146879867738/1092727)
(1468101287306546764696/25, -50161939222843006796691056019456/125)
(-16235204718794969498, -141242726468270137077539736174)
(626280733527873158017873/1024, -495055250554019749601415821375604057/32768)
(67285027167857791957/4, -30596153005382997871109675625/8)
(10447910827250046086047, -1067929157581455412417381044242886)
(55648205948048214190, -365445477283145176147818469338)
(-29664465237868792411439/1024, 3449012461664244070647372811863399/32768)
(95847927910598700085774/5041, 5151299037151256237106317672530902/357911)
(-32733699177731423706, -60130463103411986355251273298)
(4906541600493839920737/64, -321133659522007616750947280166705/512)
(2468673277758058293196/169, -38822175322691032175678480476536/2197)
(-235365675372445335629/9, -3310675860818500221415681145404/27)
(-356379588939416417391272/11449, 103380838362686601121140685689211152/1225043)
(1384422965100927289048/81, 2402924760526371365888969344640/729)
(2161931297928350680422/121, 8633826199848616733749956817254/1331)
(-936505822097003018, 104013226621511947324734290334)
(423959818435143879726/25, 429194268628778253434798439774/125)
(21415410442756481782, -32399844934057915695316404066)
(12786298158686361160, 29698841440181809829028950712)
(17021020559574885484, 3336006367854925762545771912)
(54730932748769021830, -354925983703842256401706009038)
(4810361843561909850, 76770950019918464543717334162)

Commentary

SX1008/D504, T=583/161

last edited by Andrii Prokhorenkov at 2026-10-11 00:57:15 UTC · history